Get width of properties panel
Area.width

The screen is made up of areas, each area has an x, y, width, height attribute. 

Python console test code: 

&gt;&gt;&gt; for a in C.screen.areas:
...     a.type, a.width
...     
('PROPERTIES', 346)
('CONSOLE', 931)
('VIEW_3D', 346)
('TEXT_EDITOR', 931)


Region.width

within each area there are regions. Commonly there are 'HEADER', 'UI', 'TOOLS' and 'WINDOW' regions.  For the 'VIEW_3D' region the N panel is region type  'UI'

&gt;&gt;&gt; for a in C.screen.areas:
...     if a.type == 'VIEW_3D':
...         break
...         
&gt;&gt;&gt; a.type
'VIEW_3D'

&gt;&gt;&gt; for r in a.regions:
...     r.type, r.width
...     
('HEADER', 931)
('TOOLS', 1)
('UI', 335)
('WINDOW', 931)


If you are writing UI code to go in the N panel then can get the width directly with

context.region.width


Related:

Is there a way to determine the left 3D view sidebar&#39;s current width with python?